Pre-distortion method for telecommunication system and transmitter for mobile terminal of MC-CDMA telecommunication system

ABSTRACT

The invention concerns a pre-distortion method for a telecommunication system comprising a base station and at least one user. Each symbol of said user is spread with a coding sequence over a plurality of carriers to produce a plurality of corresponding frequency components of a signal (S i (t)) to be transmitted over an uplink transmission channel to said base station. Each of said frequency components is weighted by a weighting coefficient (ω i (l)), said weighting coefficients being determined from the channel response coefficients (h i (l)) of the corresponding downlink transmission channel at the respective frequencies of said carriers and from a value of the noise variance (σ 2 ) affecting said carriers.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method for uplink pre-distortion for a Multi-Carrier Code Division Multiple Access (MC-CDMA) telecommunication system.

2. Description of the Related Art

MC-CDMA has been receiving widespread interest for wireless broadband multimedia applications. Multi-Carrier Code Division Multiple Access (MC-CDMA) combines OFDM (Orthogonal Frequency Division Multiplex) modulation and the CDMA multiple access technique. This multiple access technique was proposed for the first time by N. Yee et al. in the article entitled “Multicarrier CDMA in indoor wireless radio networks” which appeared in Proceedings of PMIC'93, Vol. 1, pages 109-113, 1993. The developments of this technique were reviewed by S. Hara et al. in the article entitled “Overview of Multicarrier CDMA” published in IEEE Communication Magazine, pages 126-133, December 1997.

Unlike DS-CDMA (Direct Spread Code Division Multiple Access), in which the signal of each user is multiplied in the time domain in order to spread its frequency spectrum, the signature here multiplies the signal in the frequency domain, each element of the signature multiplying the signal of a different sub-carrier.

In general, MC-CDMA combines the advantageous features of CDMA and OFDM, i.e. high spectral efficiency, multiple access capabilities, robustness in presence of frequency selective channels, high flexibility, narrow-band interference rejection, simple one-tap equalisation, etc.

More specifically, FIG. 1 illustrates the structure of an MC-CDMA transmitter for a given user i. We consider here the uplink, i.e. we suppose that the transmitter is located in the mobile terminal (denoted MT) of a user i. Let d_(i)(n) be the symbol to be transmitted from user i at time nT to the base station, where d_(i)(n) belongs to the modulation alphabet. The symbol d_(i)(n) is first multiplied at 110 by the a spreading sequence (and a scrambling sequence which is here omitted for the sake of clarity) denoted c_(i)(t). The spreading sequence consists of N “chips”, each “chip” being of duration T_(c), the total duration of the spreading sequence corresponding to a symbol period T. Without loss of generality, we assume otherwise specified in the following that a single spreading sequence is allocated to the user. In general, a user may be allocated one or a plurality of orthogonal spreading sequences (multi-code allocation) according to the data rate required. In order to mitigate intra-cell interference, the spreading allocated to different users are preferably chosen orthogonal.

The result of the multiplication of the symbol d_(i)(n), hereinafter simply denoted d_(i) by the elements of the spreading sequence gives N symbols multiplexed in 120 over a subset of N frequencies of an OFDM multiplex. In general the number N of frequencies of said subset is a sub-multiple of the number L of frequencies of the OFDM multiplex. We assume in the following that L=N and denote c_(i)(l)=c_(i)(lT_(c)), l=0, . . . , L−1 the values of the spreading sequence elements for user i. The block of symbols multiplexed in 120 is then subjected to an inverse fast Fourier transformation (IFFT) in the module 130. In order to prevent intersymbol interference, a guard interval of length typically greater than the duration of the impulse response of the transmission channel, is added to the MC-CDMA symbol. This is achieved in practice by adding a prefix (denoted Δ) identical to the end of the said symbol. After being serialised in the parallel to serial converter 140, the MC-CDMA symbols are converted into an analogue signal which is then filtered and RF frequency up-converted (not shown) before being amplified in amplifier 150 and transmitted over the uplink transmission channel. The MC-CDMA method can essentially be regarded as a spreading in the spectral domain (before IFFT) followed by an OFDM modulation.

The signal S_(i)(t) at time t which is supplied to the amplifier before being transmitted over the reverse link transmission channel can therefore be written, if we omit the prefix:

$\begin{matrix} {{S_{i}(t)} = {{d_{i}{\sum\limits_{l = 0}^{L - 1}\;{{c_{i}(l)}{\exp\left( {{j \cdot 2}\pi\; f_{l}t} \right)}\mspace{14mu}{for}\mspace{14mu}{nT}}}} \leq t < {\left( {n + 1} \right)T}}} & (1) \end{matrix}$ where f_(l)=(l−L/2)/T, l=0, . . . , L−1 are the frequencies of the OFDM multiplex. More precisely, it should be understood that the transmitted signal is in fact Re(S_(i)(t)exp(j2πF₀t)) where Re(.) stands for the real part and F₀ is the RF carrier frequency. In other words, S_(i)(t) is the complex envelope of the transmitted signal.

An MC-CDMA receiver for a given user i has been illustrated schematically in FIG. 2. Since we consider the uplink, the receiver is located at the base station.

After baseband demodulation, the signal is sampled at the “chip” frequency and the samples belonging to the guard interval are eliminated (elimination not shown). The signal obtained can be written:

$\begin{matrix} {{R(t)} = {{{\sum\limits_{i = 0}^{K - 1}{\sum\limits_{l = 0}^{L - 1}\;{{h_{i}(l)} \cdot {c_{i}(l)} \cdot d_{i} \cdot {\exp\left( {{j \cdot 2}\pi\; f_{l}t} \right)}}}} + {{b(t)}\mspace{14mu}{for}\mspace{14mu}{nT}}} \leq t < {\left( {n + 1} \right)T}}} & (2) \end{matrix}$ where t takes successive sampling time values, K is the number of users and h_(i)(l) represents the response of the channel of the user i to the frequency of the subcarrier l of the MC-CDMA symbol transmitted at time n.T and where b(t) is the received noise.

The samples obtained by sampling the demodulated signal at the “chip” frequency are serial to parallel converted in 210 before undergoing an FFT in the module 220. The samples in the frequency domain, output from 220, are despread by the spreading sequence of user i. To do this, the samples of the frequency domain are multiplied by the coefficients c_(i)*(l) (here in the multipliers 230 ₀, . . . , 230 _(L−1)) and then added (in adder 240). The summation result is detected in 250 for supplying an estimated symbol {circumflex over (d)}_(i). Although not represented, the detection may comprise an error correction decoding like a Viterbi or a turbo-decoding which are known as such.

Furthermore, in MC-CDMA as in DS-CDMA, equalisation can be performed at the receiving side in order to compensate for the dispersive effects of the transmission channel. In MC-CDMA, the samples in the frequency domain are respectively multiplied with equalising coefficients q_(i)(l), l=0, . . . , L−1 (here in 230 ₀, . . . , 230 _(L−1)). However, in MC-CDMA in contrast to DS-CDMA, there is no simple equalisation method for an uplink channel because the estimation of an uplink channel appears very complex.

Indeed in MC-CDMA, this estimation must be performed before despreading, i.e. at the chip level, when the signal from the different users are still combined. In contrast, in DS-CDMA, this estimation is usually performed after despreading, i.e. at the symbol level, and therefore separately for each user.

In order to overcome the problem of channel estimation, it has been proposed to implement a pre-distortion at the transmitter side (i.e. in the mobile terminal, denoted MT), so that a simple demodulator could be used at the receiver side without needing to estimate the channel. The basic idea underlying pre-distortion is to exploit the reciprocity of the transmission channels (in TDD), that is the downlink channel estimation performed for the downlink demodulation is used as an estimation of the uplink channel. This implies both TDD-operation (same frequency band used for the uplink and downlink), and relatively low MT mobility, i.e. low Doppler frequency.

An MC-CDMA TDD-system with (downlink) pre-distortion has been described e.g. in the article of D. G. Jeong et al. entitled “Effects of channel estimation error in MC-CDMA/TDD systems” published in VTC 2000-Spring Tokyo, IEEE 51^(st, Vol.) 3, pages 1773-1777. Pre-distortion is simply effected by multiplying each frequency component of the MC-CDMA symbol to be transmitted by the inverse of the channel response coefficient at said frequency, i.e. h_(i) ⁻¹(l). However, contrary to what is put forward in the above mentioned paper such downlink pre-distortion is not possible since the base station (denoted BS) cannot send one common pre-distorted multi-user signal which would have been optimised for the different propagation downlink channels from the base station to the mobile terminals (h_(i) ⁻¹(l) depends on i). This problem does not exist for the uplink transmission channels and one could think to apply this pre-distortion technique for the uplink. However, multiplying the frequency components by the coefficients h_(i) ⁻¹(l) may lead to a very high transmitted power if the uplink transmission channel exhibits deep fades (i.e. h_(i)(l) may be close to zero for some subcarriers l). This high transmitted power decreases in turn the battery autonomy and may significantly increase the interference towards adjacent cells.

SUMMARY OF THE INVENTION

An object of the present invention is to design a simple pre-distortion technique for an uplink channel in an MC-CDMA system which does not present the drawbacks set out above.

To this end, the invention is defined by the pre-distortion method claimed in claim 1 and a transmitter implementing such pre-distortion method as claimed in claim 10. Advantageous embodiments of the invention are defined in the dependent claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The characteristics of the invention will emerge from a reading of the following description given in relation to the accompanying figures, amongst which:

FIG. 1 depicts schematically the structure of an MC-CDMA transmitter known from the state of the art;

FIG. 2 depicts schematically the structure of an MC-CDMA receiver known from the state of the art;

FIG. 3 depicts schematically the structure of an MC-CDMA transmitter according to the invention;

FIG. 4 depicts schematically the structure of an MC-CDMA receiver to be used with the MC-CDMA transmitter according to the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The basic idea underlying the invention stems from the analogy between the pre-distortion and the demodulation issues. In both cases, the channel selectivity destroys the orthogonality of the spreading sequences and orthogonality must be restored without unduly increasing the noise level (in the demodulation case), or without unduly increasing the transmitting power (in the pre-distortion case).

We refer back to the context of an MC-CDMA TDD telecommunication system and more specifically to a base station receiving complex symbols from a plurality of active users i=0, . . . , K−1. Let us denote, for user i, d_(i) the (complex scalar) transmitted symbol, c_(i) the vector of components c_(i)(l), h_(i) the channel response vector of components h_(i)(l), w_(i) a pre-distortion vector of pre-distortion coefficients w_(i)(l) and ω_(i) the corresponding vector of weighting coefficients ω_(i)(l)=w_(i)*(l). In general, c_(i), h_(i) w_(i) and ω_(i) are vectors of size N, where N is the spreading sequence length. As mentioned above, it is assumed that N=L, i.e. that the code sequence length is equal to the number of carriers and that one active user uses only one code sequence. However, the results set out below can be extended to the case where the number of carriers is greater than the spreading length (typically a multiple thereof) and/or to multi-code transmission.

After FFT, the received signal can be expressed as (see equation 2):

$\begin{matrix} {y = {{{\sum\limits_{j = 0}^{K - 1}{d_{j}\left( {\omega_{j} \circ h_{j} \circ c_{j}} \right)}} + \eta} = {{\sum\limits_{j = 0}^{K - 1}{d_{j}\left( {w_{j}^{*} \circ h_{j} \circ c_{j}} \right)}} + \eta}}} & (3) \end{matrix}$ where η is a vector of AWGN components of variance σ² and where · expresses the vector multiplication element by element, that is (x·y)_(k)=x_(k)·y_(k).

The determination of the uplink channel responses being very difficult to achieve, the receiver of the base station simply demodulates the received signal by despreading it with each code sequence. The estimation of the symbol transmitted by the i^(h) user can be expressed as:

$\begin{matrix} {{\hat{d}}_{i} = {{{\mu c}_{i}^{H}y} = {{\mu{\sum\limits_{j = 0}^{K - 1}{d_{j}{c_{i}^{H} \cdot \left( {w_{j}^{*} \circ h_{j} \circ c_{j}} \right)}}}} + {{\mu c}_{i}^{H}\eta}}}} & (4) \end{matrix}$ where μ is a normalisation coefficient which for example represents the gain of the automatic gain control (AGC). As the code sequences are assumed to be normalised, η_(i)=c_(i) ^(H)η has a variance equal to σ². The expression (4) can be simplified by introducing a set of vectors v_(ij) where: v _(ij) =c _(i) *·h _(j) ·c _(j)  (5) Since the code sequences are assumed normalised and of constant amplitude, it can be noted that

$v_{ii} = {\frac{1}{N}{h_{i}.}}$ Therefore the estimation of symbol d_(i) can then be rewritten as:

$\begin{matrix} {{\hat{d}}_{i} = {{\mu{\sum\limits_{j}{d_{j}\left( {w_{j}^{H} \cdot v_{ij}} \right)}}} + {\mu\eta}_{i}}} & (6) \end{matrix}$ The power used by the mobile terminal i for transmitting the symbol d_(i) can be expressed as: P _(i) =|w _(i)|² =w _(i) ^(H) ·w _(i)  (7) The interference term MAI_(i) (due to the users j≠i) is equal to:

$\begin{matrix} {{MAI}_{i} = {\mu{\sum\limits_{j \neq i}\;{d_{j}\left( {w_{j}^{H} \cdot v_{ij}} \right)}}}} & (8) \end{matrix}$ whereas the useful term is equal to:

$\begin{matrix} {{\overset{\sim}{d}}_{i} = {{\mu\; d_{i}w_{i}^{H}v_{ii}} = {\frac{\mu}{N}d_{i}w_{i}^{H}h_{i}}}} & (9) \end{matrix}$

The purpose of the invention is to find the vector w_(i) of pre-distortion coefficients which maximises the value of {tilde over (d)}_(i), while minimising the interference MAI_(i) and transmitted power P_(i). According to the invention, it is proposed to minimise a global mean square error taking into account all the users under the constraint of a fixed transmitted power for each user. The power control loop between the mobile terminal of user i and the base station ensures that the product of the transmitted power by the channel attenuation is maintained about a desired value which is the same for all the active users. Without loss of generality, we may equivalently suppose in the following that the transmitted power is the same for all the users, e.g. equal to N (that is the average power of each carrier is chosen equal to 1) and that the channel attenuation is identical for all the channels. Let us consider the cost function:

$\begin{matrix} {J = {\sum\limits_{i}{E\left( {{\hat{d}}_{i} - d_{i}} \right)}^{2}}} & (10) \end{matrix}$

The problem of minimisation under constraint mentioned above amounts to finding the minimum of the Lagrange function:

$\begin{matrix} {L = {{\sum\limits_{i}{E\left( {{\hat{d}}_{i} - d_{i}} \right)}^{2}} + {\sum\limits_{i}{\lambda_{i}\left( {{w_{i}^{H} \cdot w_{i}} - N} \right)}}}} & (11) \end{matrix}$ where the λ_(i) are the Lagrange scalar multipliers.

The error on the estimation {circumflex over (d)}_(i)−d_(i) can be obtained from (6) and (8):

$\begin{matrix} {{{\hat{d}}_{i} - d_{i}} = {{d_{i}\left( {{{\mu w}_{i}^{H} \cdot v_{ii}} - 1} \right)} + {\mu{\sum\limits_{j \neq i}\;{d_{j}\left( {w_{j}^{H} \cdot v_{ij}} \right)}}} + {\mu\eta}_{i}}} & (12) \end{matrix}$ The coefficient μ has to be optimised: for normalised transmission and channels, the amplitude of the useful part will depend on the pre-distortion method, and be equal to 1 only for w_(i)=h_(i). A bias will therefore be introduced, and must be compensated by AGC before calculation of the square error. From (12), the global mean square error can be estimated:

$\begin{matrix} {{E\left( {{\hat{d}}_{i} - d} \right)}^{2} = {{\mu^{2}w_{i}^{H}v_{ii}v_{ii}^{H}w_{i}} + 1 - {{\mu w}_{i}^{H}v_{ii}} - {{\mu v}_{ii}^{H}w_{i}} + {\mu^{2}{\sum\limits_{j \neq i}{w_{j}^{H}v_{ij}v_{ij}^{H}w_{j}}}} + {\mu^{2}\sigma^{2}}}} & (13) \\ {{E\left( {{\hat{d}}_{i} - d} \right)}^{2} = {{\mu^{2}{\sum\limits_{j}{w_{j}^{H}v_{ij}v_{ij}^{H}w_{j}}}} + 1 - {{\mu w}_{i}^{H}v_{ii}} - {{\mu v}_{ii}^{H}w_{i}} + {\mu^{2}\sigma^{2}}}} & (14) \\ {{~~~~~~~~~~~~~~~~~~~~}{L = {{\mu^{2}{\sum\limits_{i}{\sum\limits_{j}{w_{j}^{H}v_{ij}v_{ij}^{H}w_{j}}}}} + K - {\mu{\sum\limits_{i}{w_{i}^{H}v_{ii}}}} - {\mu{\sum\limits_{i}{v_{ii}^{H}w_{i}}}} + {K\;\mu^{2}\sigma^{2}} + {\sum\limits_{i}{\lambda_{i}\left( {{w_{i}^{H}w_{i}} - N} \right)}}}}} & (15) \end{matrix}$ The first term of (15) can be rewritten as:

$\begin{matrix} {{\sum\limits_{i}{\sum\limits_{j}{w_{j}^{H}v_{ij}v_{ij}^{H}w_{j}}}} = {{\sum\limits_{i}{\sum\limits_{j}{w_{i}^{H}v_{ji}v_{ji}^{H}w_{i}}}} = {{\sum\limits_{i}{{w_{i}^{H}\left( {\sum\limits_{j}{v_{ji}v_{ji}^{H}}} \right)}w_{i}}} = {\sum\limits_{i}{w_{i}^{H}\Phi_{i}w_{i}}}}}} & (16) \end{matrix}$ where the Hermitian matrix Φ_(i) is defined as:

$\begin{matrix} {\Phi_{i} = {\sum\limits_{j}{v_{ji}v_{ji}^{H}}}} & (17) \end{matrix}$ Finally, the Lagrange function is expressed as:

$\begin{matrix} {L = {{\mu^{2}{\sum\limits_{i}{w_{i}^{H}\Phi_{i}w_{i}}}} + K - {\mu{\sum\limits_{i}{w_{i}^{H}v_{ii}}}} - {\mu{\sum\limits_{i}{v_{ii}^{H}w_{i}}}} + {K\;\mu^{2}\sigma^{2}} + {\sum\limits_{i}{\lambda_{i}\left( {{w_{i}^{H}w_{i}} - N} \right)}}}} & (18) \end{matrix}$

By calculating the gradients according to the vectors w_(i)*=ω_(i) (the same result is obtained by calculating the gradients according to vector w_(i)), the following set of equations is obtained: ∇_(w) _(i) ·L=μ ²Φ_(i) w _(i) −μv _(ii)+λ_(i) w _(i)=0 for 0≦i>K−1  (19) By replacing v_(ii) with h_(i)/N:

$\begin{matrix} {{\left( {{\mu^{2}\Phi_{i}} + {\lambda_{i}I}} \right)w_{i}} = {\frac{\mu}{N}h_{i}}} & (20) \end{matrix}$ where I is the identity matrix of size N×N. At that stage, parameters λ_(i) and μ remain to be determined. Deriving L according to parameters μ provides a new equation:

$\begin{matrix} {{{\partial L}/{\partial\mu}} = {{{2\mu{\sum\limits_{i}{w_{i}^{H}\Phi_{i}w_{i}}}} - {\sum\limits_{i}{w_{i}^{H}v_{ii}}} - {\sum\limits_{i}{v_{ii}^{H}w_{i}}} + {2K\;{\mu\sigma}^{2}}} = 0}} & (21) \end{matrix}$ By combining equations (20) and (21), we obtain:

$\begin{matrix} {{{2{\sum\limits_{i}{{w_{i}^{H}\left( {{\frac{1}{N}h_{i}} - {\frac{\lambda_{i}}{\mu}w_{i}}} \right)}\frac{1}{N}{\sum\limits_{i}{w_{i}^{H}h_{i}}}}}} - {\frac{1}{N}{\sum\limits_{i}{h_{i}^{H}w_{i}}}} + {2K\;{\mu\sigma}^{2}}} = 0} & (22) \\ {{{\frac{1}{N}{\sum\limits_{i}{w_{i}^{H}h_{i}}}} - {\frac{1}{N}{\sum\limits_{i}{h_{i}^{H}w_{i}}}} - {\frac{2}{\mu}{\sum\limits_{i}{\lambda_{i}{w_{i}}^{2}}}} + {2K\;{\mu\sigma}^{2}}} = 0} & (23) \end{matrix}$ Furthermore, by multiplying on the left each term of equation (20) by w_(i) ^(H), we obtain:

$\begin{matrix} {{{\mu^{2}w_{i}^{H}\Phi_{i}w_{i}} + {\lambda_{i}{w_{i}}^{2}}} = {\frac{\mu}{N}w_{i}^{H}h_{i}}} & (24) \end{matrix}$ As Φ_(i) is Hermitian, the left-hand term of (24) is real, and therefore w_(i) ^(H)h_(i) is real and equal to h_(i) ^(H)w_(i). A simple expression between the λ_(t) and μ is obtained:

$\begin{matrix} {{K\;\mu^{2}\sigma^{2}} = {\sum\limits_{i}{\lambda_{i}{w_{i}}^{2}}}} & (25) \end{matrix}$ Since the transmitted power |w_(i)|² is assumed to be equal to N:

$\begin{matrix} {{K\;\mu^{2}\sigma^{2}} = {{\sum\limits_{i}\lambda_{i}} = {{NK}\overset{\_}{\lambda}}}} & (26) \end{matrix}$ where λ is the average value of the Lagrange multipliers λ_(i). The average value λ can therefore be expressed as:

$\begin{matrix} {\overset{\_}{\lambda} = \frac{\mu^{2}\sigma^{2}}{N}} & (27) \end{matrix}$ Let us recall that each Lagrange multiplier λ_(i) must be chosen so that each transmitted power |w_(i)|² is equal to N. It is very difficult in practice to determine precisely the λ_(i) and μ values from equations (20) and (25). According to the invention it is proposed to approximate in equation (20) the λ_(i) values by the mean value λ. Equation (20) then becomes:

$\begin{matrix} {w_{i} = {{\frac{\mu}{N}\left( {{\mu^{2}\Phi_{i}} + {\overset{\_}{\lambda}I}} \right)^{- 1}h_{i}} = {{\frac{\mu}{N}\left( {{\mu^{2}\Phi_{i}} + {\frac{\mu^{2}\sigma^{2}}{N}I}} \right)^{- 1}h_{i}} = {\frac{1}{\mu\; N}\left( {\Phi_{i} + {\frac{\sigma^{2}}{N}I}} \right)^{- 1}h_{i}}}}} & (28) \end{matrix}$

Due to the above approximation, equation (28) could provide a solution with a transmitted power slightly different from N. In addition, the transmitter does not know the value of parameter μ. In practice, the transmitter of user i solves the linear system of equations (28) i.e. determines the unknown pre-distortion vector w_(i) and normalises the result so that |w_(i)|² is equal to N. Therefore,

$\begin{matrix} {w_{i} = {{\alpha\left( {\Phi_{i} + {\frac{\sigma^{2}}{N}I}} \right)}^{- 1}h_{i}}} & (29) \end{matrix}$ where the real coefficient α corresponds to the normalisation of w_(i).

Equivalently, instead of inverting the matrix

$\Phi_{i} + {\frac{\sigma^{2}}{N}I}$ a system of N linear equations corresponding to

${{\left( {\Phi_{i} + {\frac{\sigma^{2}}{N}I}} \right)w_{i}} = h_{i}},$ and where w_(i)(l) are the unknown coefficients, can be solved. The pre-distortion coefficients w_(i)(l) are then normalised as set out above. The weighting coefficients are then obtained from ω_(i)(l)=w_(i)*(l).

Because of the presence of the matrix

$\frac{\sigma^{2}}{N}I$ in expression (29) the pre-distortion coefficients w_(i)(l) are bounded even if a deep fade is experienced on the transmission channel. The value of the noise variance σ² is taken here as the inverse of the SINR (Signal to Interference plus Noise Ratio) for the demodulated signal. It can be estimated by the base station and transmitted to the mobile terminal. Alternatively, a value of the noise variance σ² can be retrieved from a look-up table of typical values stored e.g. in a memory of the mobile terminal. In general, the table is indexed by the parameters of the communication as the targeted BER level, the type of modulation, the type of channel coding used.

The matrix Φ_(i) for user i can be expressed as a function of the code sequences c_(j) (for all the users j) and channel response h_(i) as follows:

$\begin{matrix} {\Phi_{i} = {{\sum\limits_{j}{v_{ji}v_{ji}^{H}}} = {\sum\limits_{j}{\left( {c_{j}^{*} \circ h_{i} \circ c_{i}} \right)\left( {c_{j}^{*} \circ h_{i} \circ c_{i}} \right)^{H}}}}} & (30) \\ {\Phi_{i} = {\sum\limits_{j}{{{{Diag}\left( h_{i} \right)} \cdot {{Diag}\left( c_{i} \right)} \cdot \left( {c_{j}^{*}c_{j}^{T}} \right)}{{{Diag}\left( c_{i}^{*} \right)} \cdot {{Diag}\left( h_{i}^{*} \right)}}}}} & (31) \end{matrix}$ where .^(T) denotes the transpose operation and Diag(u) denotes the diagonal matrix having the components of the vector u as diagonal elements.

$\begin{matrix} {\Phi_{i} = {{{Diag}\left( h_{i} \right)} \cdot {{Diag}\left( c_{i} \right)} \cdot {\sum\limits_{j}{\left( {c_{j}^{*}c_{j}^{T}} \right) \cdot {{Diag}\left( c_{i}^{*} \right)} \cdot {{Diag}\left( h_{i}^{*} \right)}}}}} & (32) \end{matrix}$ and therefore: Φ_(i)=Diag(h _(i))·Diag(c _(i))·C*C ^(T)·Diag(c _(i)*)·Diag(h _(i)*)  (33) where C is the N×K matrix of the code sequences.

As it can be seen from expression (33), the calculation of Φ_(i) merely entails a multiplication by diagonal matrices which requires few simple operations, and the calculation of the matrix C*C^(T) for which fast algorithms, e.g. Fast Fourier Transform (FFT) or Walsh Hadamard Transform (WHT) do exist. The latter matrix needs only to be recalculated when the number of users or the code allocation changes, for example every frame. It is important to note that the matrix Φ_(i) and hence the vector w_(i) does not depend on the vectors of channel coefficients h_(j), j≠i. The transmitter of the mobile terminal i simply needs to know the codes of the active users and the coefficients of the uplink channel for user i. As indicated above, the coefficients of the uplink channel are supposed identical to those of the downlink channel.

FIG. 3 illustrates the structure of a MC-CDMA transmitter implementing the uplink pre-distortion method according to the invention. As in the prior art, the transmitter comprises a first multiplier 310 for multiplying the symbol to be transmitted by the code sequence of user i, a multiplexer 320 for multiplexing the results over the OFDM multiplex, a module 330 performing an inverse Fourier transform (with prefix insertion), a parallel/serial converter 340 and an amplifier 350. In contrast with the prior art however, the transmitter further comprises a second multiplier 311 for multiplying the frequency components d_(i)c_(i)(l) with the weighting coefficients ω_(i)(l)=w_(i)*(l) respectively. A channel estimation module 360 estimates, e.g. from a received signal corresponding to a pilot symbol transmitted by the base station, the channel coefficients h_(i)(l). From these coefficients and the knowledge of the code sequences allocated to the K active users, the matrix Φ_(i) is calculated in module 361 according to equation (33). From the matrix Φ_(i), the vector h_(i) and a value of noise variance σ² the module 362 determines the pre-distortion coefficients w_(i)(l) according to expression (29) and then the weighting coefficients ω_(i)(l)=w_(i)*(l).

According to a first variant of the invention shown below, the calculation of the matrix Φ_(i) in module 361 can be made in the real domain. Indeed, if h_(i)(l)=ρ_(i)(l)e^(jθ) ^(i) ^((l)) where ρ_(i)(l) and θ_(i)(l) are respectively the amplitude and the argument of the channel response coefficient h_(i)(l), and we denote ρ_(i) and e^(jθ) ^(i) the vectors of components ρ_(i)(l) and e^(jθ) ^(i) ^((l)) respectively, we have: Φ_(i)=Diag(e ^(jθ) ^(i) )Φ_(i)Diag(e ^(−jθ) ^(i) )  (34) where we have denoted: Φ_(i)=Diag(ρ_(i))·Diag(c _(i))·C*C ^(T)·Diag(c _(i)*)·Diag(ρ _(i))  (35) From equation (34) we obtain:

$\begin{matrix} {w_{i} = {{\alpha\left( {{{{Diag}\left( {\mathbb{e}}^{{j\theta}_{i}} \right)} \cdot \Phi_{i}^{\prime} \cdot {{Diag}\left( {\mathbb{e}}^{- {j\theta}_{i}} \right)}} + {\frac{\sigma^{2}}{N}I}} \right)}^{- 1}h_{i}}} \\ {w_{i} = {{\alpha\left( {{{Diag}\left( {\mathbb{e}}^{{j\theta}_{i}} \right)} \cdot \left( {\Phi_{i}^{\prime} + {\frac{\sigma^{2}}{N}I}} \right) \cdot {{Diag}\left( {\mathbb{e}}^{- {j\theta}_{i}} \right)}} \right)}^{- 1}h_{i}}} \\ {w_{i} = {{{{\alpha Diag}\left( {\mathbb{e}}^{{j\theta}_{i}} \right)} \cdot \left( {\Phi_{i}^{\prime} + {\frac{\sigma^{2}}{N}I}} \right)^{- 1} \cdot {{Diag}\left( {\mathbb{e}}^{- {j\theta}_{i}} \right)}}h_{i}}} \\ {w_{i} = {{{{\alpha Diag}\left( {\mathbb{e}}^{{j\theta}_{i}} \right)} \cdot \left( {\Phi_{i}^{\prime} + {\frac{\sigma^{2}}{N}I}} \right)^{- 1}}\rho_{i}}} \end{matrix}$ Hence, 107 _(i)=Diag(e ^(−jθ) ^(i) )ω_(i)′  (36) where

$\omega_{i}^{\prime} = {{\alpha \cdot \left( {\Phi_{i}^{\prime} + {\frac{\sigma^{2}}{N}I}} \right)^{- 1}}{\rho_{i}.}}$ It is therefore possible to make the calculation in 361 and 362 in the real domain and to apply last the phase factors e^(−jθ) ^(i) ^((l)) to the real components ω_(i)′(l).

A second variant of the invention is described hereafter. First, it is assumed that the MC-CDMA operates at full load and the code sequences are orthogonal or quasi-orthogonal. In such instance the matrix C*C^(T) is equal to the identity matrix and (33) then becomes:

$\begin{matrix} {\Phi_{i} = {{{Diag}\left( {{h_{i}}^{2}{c_{i}}^{2}} \right)} = {\frac{1}{N}{{Diag}\left( {h_{i}}^{2} \right)}}}} & (37) \end{matrix}$ By replacing the expression (37) into (29), we obtain for the full load case a pre-distortion vector of components w_(i)(l):

$\begin{matrix} {{w_{i}(l)} = {\alpha\; N\frac{h_{i}(l)}{{{h_{i}(l)}}^{2} + \sigma^{2}}}} & (38) \end{matrix}$ where α is a normalisation factor. In such instance, the weighting coefficients are expressed as:

$\begin{matrix} {{\omega_{i}(l)} = {\alpha\; N\frac{h_{i}^{*}(l)}{{{h_{i}(l)}}^{2} + \sigma^{2}}}} & (39) \end{matrix}$

When the system does not operate at full load, the matrix C*C^(T) is not equal to the identity matrix anymore but the diagonal terms remain predominant. Indeed, the diagonal terms are equal to:

$\begin{matrix} {\gamma_{kk} = {{\sum\limits_{j = 0}^{K - 1}\;{C_{kj}^{*}C_{kj}}} = \frac{K}{N}}} & (40) \end{matrix}$ and are expected to be larger than the off-diagonal terms

$\gamma_{{kk}^{\prime}} = {\sum\limits_{j = 0}^{K - 1}\;{C_{kj}^{*}C_{k^{\prime}j}}}$ since the terms C*_(kj)C_(k′j) tend to cancel out each other when k≠k′. By approximating the matrix C*C^(T) to its diagonal terms, we obtain:

$\begin{matrix} {{\Phi \approx {{Diag}\left( {\frac{K}{N}{h_{i}}^{2}{c_{i}}^{2}} \right)}} = {\frac{K}{N^{2}}{{Diag}\left( {h_{i}}^{2} \right)}}} & (41) \end{matrix}$ Finally, by replacing expression (41) into (29), the components of the pre-distortion vector, can be approximated as follows:

$\begin{matrix} {{{w_{i}(l)} \approx {{\alpha\left\lbrack {{\frac{K}{N^{2}}{{h_{i}(l)}}^{2}} + \frac{\sigma^{2}}{N}} \right\rbrack}^{- 1}{h_{i}(l)}}} = {\alpha\frac{N^{2}}{K}\frac{h_{i}(l)}{{{h_{i}(l)}}^{2} + {\frac{N}{K}\sigma^{2}}}}} & (42) \end{matrix}$ where α is a normalisation factor. That is, the weighting coefficients ω_(i)(l) are expressed as:

$\begin{matrix} {{w_{i}(l)} = {\alpha\frac{N^{2}}{K}\frac{h_{i}^{*}(l)}{{{h_{i}(l)}}^{2} + {\frac{N}{K}\sigma^{2}}}}} & (43) \end{matrix}$

In addition, it can be shown that, if the channel response coefficients h_(i)(l), l=0, . . . , L−1 are correlated, the MAI level is reduced and the following expression for the weighting coefficients is advantageously used:

$\begin{matrix} {{\omega_{i}(l)} = {\alpha\frac{N^{2}}{K}\frac{h_{i}^{*}(l)}{{\beta.{{h_{i}(l)}}^{2}} + {\frac{N}{K}\sigma^{2}}}}} & (44) \end{matrix}$ where β is a weighting factor, 0≦β≦1, which reflects the correlation of the channel response coefficients h_(i)(l), l=0, . . . , L−1 and departs from β=1 when the channel response coefficients are correlated.

FIG. 4 illustrates the structure of a MC-CDMA receiver in the base station adapted to receive a signal transmitted by a MC-CDMA transmitter according to the invention. As in the prior art of FIG. 2, the present receiver comprises a serial to parallel converter 410, an FFT module 420 (with prefix removal), multipliers 430 ₀ to 430 _(L−1) for multiplying the samples in the frequency domain by the conjugates c_(i)*(l) of the elements of the spreading sequence, an adder 440 and a detector 450 for supplying the estimated symbols. As in the prior art, an error control decoding can be provided, like a Viterbi decoding or a turbo-decoding. In contrast to the prior art, however, no equalisation is needed since pre-distortion has been performed at the transmitter side.

Although the MC-CDMA transmitter illustrated in FIG. 3 has been described in terms of functional modules e.g. computing or estimating means, it goes without saying that all or part of this device can be implemented by means of a single processor either dedicated for performing all the functions depicted or in the form of a plurality of processors either dedicated or programmed for each performing one or some of said functions. 

1. A method of pre-distorting a signal (S_(i)(t)) to be transmitted over an uplink transmission channel to a base station by a mobile terminal (i), each symbol (d_(i)) transmitted by said mobile terminal being spread with a coding sequence (c_(i)(l)) over a plurality of carriers (l) to produce a plurality of corresponding frequency components (d_(i)c_(i)(l)) of said signal (S_(i)(t)), comprising: weighting each frequency component (d_(i)c_(i)(l)) by a weighting coefficient (ω_(i)(l)) corresponding to one channel response coefficient (h_(i)(l)), of a plurality of channel response coefficients, of a corresponding downlink transmission channel at a corresponding frequency (f_(l)) and to a value of a noise variance (σ²) affecting said plurality of carriers, said step of weighting including, for said mobile terminal (i), determining a vector ω_(i) representing said weighting coefficients from a vector h_(i) representing said channel response coefficients as a conjugate of a vector ω_(i), vector ω_(i) being ${w_{i} = {{\alpha\left( {\Phi_{i} + {\frac{\sigma^{2}}{N}I}} \right)}^{- 1}h_{i}}},$ where I is the identity matrix, N is a length of said coding sequence, α is a normalisation factor, and Φ_(i) is a matrix depending on coding sequences allocated to active mobile terminals served by said base station and depending on said channel response coefficients.
 2. The method of claim 1, wherein Φ_(i)=Diag(h_(i))·Diag(c_(i))·C*C^(T)·Diag(c_(i)*)·Diag(h_(i)*) where Diag(h_(i)) and Diag(h_(i)*) are diagonal matrices having respectively said channel response coefficients and conjugates thereof as diagonal elements, Diag(c_(i)) and Diag(c_(i)*) are diagonal matrices having respectively elements of the coding sequence mobile terminal and conjugates thereof as diagonal elements, C is a matrix representing code sequences allocated to the active mobile terminals served by said base station, and where T denotes the transpose operation.
 3. The method of claim 1, wherein, $\Phi_{i} = {\frac{K}{N^{2}}{{Diag}\left( \left| h_{i} \right|^{2} \right)}}$ where mobile terminals Diag(|h_(i)|²) is a diagonal matrix having a square modulus of said channel response coefficients as diagonal elements.
 4. The method of claim 1, further comprising: retrieving said value of noise variance (σ²) from a look-up table.
 5. The method of claim 1, further comprising: retrieving said value of noise variance (σ²) from said base station.
 6. A method of pre-distorting a signal (S_(i)(t)) to be transmitted over an uplink transmission channel to a base station by a mobile terminal (i), each symbol (d_(i)) transmitted by said mobile terminal being spread with a coding sequence (c_(i)(l)) over a plurality of carriers (l) to produce a plurality of corresponding frequency components (d_(i)c_(i)(l)) of said signal (S_(i)(t)), comprising: weighting each frequency component (d_(i)c_(i)(l)) by a weighting coefficient (ω_(i)(l)) corresponding to one channel response coefficient (h_(i)(l)), of a plurality of channel response coefficients, of a corresponding downlink transmission channel at a corresponding frequency (f_(l)) and to a value of a noise variance (σ²) affecting said plurality of carriers, said weighting coefficient ω_(i)(l) being proportional to $\frac{h_{i}^{*}(l)}{\left. \beta \middle| {h_{i}(l)} \middle| {}_{2}{{+ \frac{N}{K}}\sigma^{2}} \right.}$ where N is a length of said code sequence, K is a number of active mobile terminals served by said base station, β is a real weighting coefficient and * denotes the conjugate operation.
 7. The method of claim 6, further comprising: retrieving said value of noise variance (σ²) from a look-up table.
 8. The method of claim 6, further comprising: receiving said value of the noise variance (σ²) from said base station.
 9. A method of pre-distorting a signal (S_(i)(t)) to be transmitted over an uplink transmission channel to a base station by a mobile terminal (i), each symbol (d_(i)) transmitted by said mobile terminal being spread with a coding sequence (c_(i)(l)) over a plurality of carriers (l) to produce a plurality of corresponding frequency components (d_(i)c_(i)(l)) of said signal (S_(i)(t)), comprising: weighting each frequency component (d_(i)c_(i)(l)) by a weighting coefficient (ω_(i)(l)) corresponding to one channel response coefficient (h_(i)(l)), of a plurality of channel response coefficients, of a corresponding downlink transmission channel at a corresponding frequency (f_(l)) and to a value of a noise variance (σ²) affecting said plurality of carriers, said step of weighting including determining, for said mobile terminal (i), a vector ω′_(i) representing respective amplitudes of resulting weighting coefficients from a vector ρ_(i) representing respective amplitudes of said channel response coefficients, with $\omega_{i}^{\prime} = {{\alpha \cdot \left( {\Phi_{i}^{\prime} + {\frac{\sigma^{2}}{N}I}} \right)^{- 1}}\rho_{i}}$ where I is the identity matrix, N is a length of said code sequence, α is a normalisation factor and Φ′_(i) is a matrix depending on coding sequences allocated to active mobile terminals served by said base station and on said channel response coefficients.
 10. The method of claim 9, wherein Φ′_(i)=Diag(ρ_(i))·Diag(c_(i))·C*C^(T)·Diag(c_(i)*)·Diag(ρ_(i)) where Diag(ρ_(i)) is a diagonal matrix having components of said vector ρ_(i) as diagonal elements, Diag(c_(i)) and Diag(c_(i)*) are diagonal matrices having respectively elements of the coding sequence of said mobile terminal and conjugates thereof as diagonal elements, C is a matrix representing the code sequences allocated to the active mobile terminals, * and .^(T) denotes a transpose operation.
 11. The method of claim 9, further comprising: retrieving said value of noise variance (σ²) from a look-up table.
 12. The method of claim 9, further comprising: receiving said value of the noise variance (σ²) from said base station.
 13. A mobile terminal (i) configured to pre-distort a signal (S_(i)(t)) prior to transmitting said signal over an uplink transmission channel to a base station, including a spreader configured to spread each symbol (d_(i)) with a coding sequence (c_(i)(l)) over a plurality of carriers (l) to produce a plurality of corresponding frequency components (d_(i)c_(i)(l)) of said signal (S_(i)(t)), comprising: a pre-distorter configured to apply a weighting coefficient (ω_(i)(l)) to each frequency component (d_(i)c_(i)(l)), the weighting coefficient (ω_(i)(l)) corresponding to one channel response coefficient (h_(i)(l)), of a plurality of channel response coefficients, of a corresponding downlink transmission channel at a corresponding frequency (f_(l)) and to a value of a noise variance (σ²) affecting said plurality of carriers, said predistorter configured to determine, for said mobile terminal (i), a vector ω_(i) representing said weighting coefficients from a vector h_(i) representing said channel response coefficients as a conjugate of a vector ω_(i), vector ω_(i) being ${w_{i} = {{\alpha\left( {\Phi_{i} + {\frac{\sigma^{2}}{N}I}} \right)}^{- 1}h_{i}}},$ where I is the identity matrix, N is a length of said coding sequence, α is a normalisation factor, and Φ_(i), is a matrix depending on coding sequences allocated to active mobile terminals served by said base station and depending on said channel response coefficients.
 14. A mobile terminal (i) configured to pre-distort a signal (S_(i)(t)) prior to transmitting said signal over an uplink transmission channel to a base station, including a spreader configured to spread each symbol (d_(i)) with a coding sequence (c_(i)(l)) over a plurality of carriers (l) to produce a plurality of corresponding frequency components (d_(i)c_(i)(l)) of said signal (S_(i)(t)), comprising: a pre-distorter configured to apply a weighting coefficient (ω_(i)(l)) to each frequency component (d_(i)c_(i)(C)), the weighting coefficient (ω_(i)(l)) corresponding to one channel response coefficient (h_(i)(l)), of a plurality of channel response coefficients, of a corresponding downlink transmission channel at a corresponding frequency (f_(l)) and to a value of a noise variance (σ²) affecting said plurality of carriers, said weighting coefficient ω_(i)(l) being proportional to $\frac{h_{i}^{*}(l)}{{\beta{{h_{i}(l)}}^{2}} + {\frac{N}{K}\sigma^{2}}}$ where N is a length of said code sequence, K is a number of active mobile terminals served by said base station, β is a real weighting coefficient and * denotes the conjugate operation.
 15. A mobile terminal (i) configured to pre-distort a signal (S_(i)(t)) prior to transmitting said signal over an uplink transmission channel to a base station, including a spreader configured to spread each symbol (d_(i)) with a coding sequence (c_(i)(l) over a plurality of carriers (l) to produce a plurality of corresponding frequency components (d_(i)c_(i)(l)) of said signal (S_(i)(t)), comprising: a pre-distorter configured to apply a weighting coefficient (ω_(i)(l)) to each frequency component (d_(i)c_(i)(l)), the weighting coefficient (ω_(i)(l)) corresponding to one channel response coefficient (h_(i)(l), of a plurality of channel response coefficients, of a corresponding downlink transmission channel at a corresponding frequency (f_(l)) and to a value of a noise variance (σ²) affecting said plurality of carriers, said predistorter configured to determine, for said mobile terminal (i), a vector ω′_(i) representing respective amplitudes of resulting weighting coefficients from a vector ρ_(i) representing respective amplitudes of said channel response coefficients, with $\omega_{i}^{\prime} = {{\alpha \cdot \left( {\Phi_{i}^{\prime} + {\frac{\sigma^{2}}{N}I}} \right)^{- 1}}\rho_{i}}$ where I is the identity matrix, N is a length of said code sequence, α is a normalisation factor and Φ′_(i) is a matrix depending on coding sequences allocated to active mobile terminals served by said base station and on said channel response coefficients. 